1. What would the slope of a line that is parallel to the line in the graph be?
(4,3)
X

Data Input

1 Adult + 2 children

The price for all three family members

$76

Procedure

Adult ticket = $28

1 Adult + 2 children = $76

2 children = 76 - 1 adult

2 children = 76 - 28

2 children = 48

children = 48/2

children = 24

Answer: (-1, 0)

The interval of decreasing refers to the interval of x-values where the graph is decreasing or going down.

If we look at the graph:

We can see that the graph starts to decrease or "go down" at values x = -1 and x=0. With this, we can conclude that the interval of decrease for the given graph is (-1, 0)

Answer:

152 cm

Step-by-step explanation:

Perimeter of kite= 2(a+b)

P= 2(AB+CD) = 2(29+47) = 2 *(76) = 152 cm.

If something remains unclear, be free to ask questions!

After conducting mathematical operations, we know that 11/3÷2/3 leaves a remainder of 5½.

So, 11/3÷2/3:

Therefore, after conducting mathematical operations, we know that 11/3÷2/3 leaves a remainder of 5½.

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Answer: No

Step-by-step explanation:

The graph fails the vertical line test, and thus the graph does not represent a function.

There would be 20 guests for the restaurants to cost the same

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

From the question, we have the following parameters:

Red Lobster

Rate per person = $30

Set up fee = $100

Olive Garden

Rate per person = $25

Set up fee = $200

So, the equations of the restaurants are

Red Lobster = 30g + 100

Olive Garden = 25g + 200

Where the number of guests is g

When the restaurants cost the same amount, we have

Red Lobster = Olive Garden

Substitute the known values in the above equation

So, we have

30g + 100 = 25g +200

Evaluate the like terms

5g = 100

Divide by 5

g = 20

Hence, the number of guests is 20

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Denominator has been factorized on the right.

Now we need to write this fraction as a sum of two fraction.

when x = 8 we have following

Similarly when x =-4 A = 17/12 these are the constants

[tex]y = -1.25 x^{2}+ 5[/tex]  is the needed quadratic function in standard form.

A quadratic equation is one with a single degree 2-variable and has the general form  [tex]a x^{2} + bx + c = 0.[/tex]  a, b, and c is the constant value, and x consists of a variable.

The quadratic equation's x-intercepts are (-5, 0). That indicated that the quadratic equation's two elements are (x + 5) and (x -0).

f(x) = a (x + 5) (x - 0) (x - 0)

= ax+5a

f(x) = [tex]ax^{2} +5x[/tex]

The quadratic equation's graph goes through (4, 0). Therefore, we must change equation 1 to read x = 4 and f(x) = 0.

0 = a × 4² + (5 × 4)

0 = a × 16 +20

a = [tex]\frac{-20}{16}[/tex]

=-1.25

The quadratic equation is known to have the form ax² + bx + c = 0.

f(x) = -1.25[tex]x^{2}[/tex] + 5x  

Consider y= F(x)

∴ The required quadratic equation of function in the standard form is Y = -1.25 x² + 5x.

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Therefore

Answer:

yes it's is shown in the diagram below and prosperity more than your expectation for me too anymore I just

The correct option is option B i.e., 36 + 9 = 3(12 + 3) is an equation representing distributive property.

What is distributive property ?

Distributive property states that the outcomes are the same whether the numbers in parenthesis are added before or after multiplication.

We know that according to the distributive property both sides must be equal such that the outcomes are same whether the numbers in parenthesis are added before or after multiplication. The expression for distributive property is given as : a(b + c) = ab + ac

So , checking the options one by one :

A) 36 + 9 = 45 ; is not an equation representing distributive property as it doesn't satisfy the criteria of a distributive property.

B) 36 + 9 = 3(12 + 3) is an equation representing distributive property as it satisfies the criteria mentioned above i.e.,

36 + 9 = 3 × 12 + 3 × 3

36 + 9 = 36 + 9

45 = 45

C) 36 x 9 = 9 x 36 is not an equation representing distributive property.

D)  (12 + 3) × 3 = 3 × (12 + 3) is not an equation representing distributive property because both sides are written in the same way.

Therefore , correct option is option B i.e., 36 + 9 = 3(12 + 3) is an equation representing distributive property.

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ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following system of equations:

To graph, we calculate the intercepts in each equation to then draw the straight line corresponding to each equation, like this:

Now we graph:

A)

In order to check this sentence, we need to convert the value from foot to yard.

Knowing that 1 yard is equal 3 feet, we have that:

So Debbie's affirmation is incorrect, therefore we disagree.

B)

First we need to calculate the area of the table cloth.

Converting the length to foot, we have:

Now, calculating the area (which is the product of the length and the width), we have:

If each square foot is $0.25, we just need to multiply the area by the cost of one square foot in order to find the cost of the fabric for the table cloth:

So the cost is $30.

Percentage of a number

Find a number which

its a 100% percentage

henW

When 232 is 290%

Then find

X = (100%/290)• 232

Divide 232/29 = 10% = 8 exactly

Now multiply by 10 = 10• 8 = 80

Then 100% = 80

Answer:

x=\frac{1}{4}(h-12y-2)x=4

Step-by-step explanation:x=\frac{1}{4}(h-12y-2)x=

4

1

(h−12y−2)

Step-by-step explanation:

We are given the equation h=4(x+3y)+2h=4(x+3y)+2 .

Simplifying for x, we get,

h=4(x+3y)+2h=4(x+3y)+2

i.e. h=4x+12y+2h=4x+12y+2

i.e. 4x=h-12y-24x=h−12y−2

i.e. x=\frac{1}{4}(h-12y-2)x=

4

1

(h−12y−2)

Thus, the equation for x is x=\frac{1}{4}(h-12y-2)x=

4

1

Given Data:

Total working hours is = 51 hours.

Pay rate=$8.45.

OT rate=1.5 times the regular pay rate.

Regular working hours is 40 hours.

Regular pay can be determined as,

Thus, the regular pay is $338.

The OT rate can be determined as,

Thus, the overtime rate is $ 12.68.

The overtime pay can be determined as,

Thus, the overtime pay is $139.43.

The gross pay can be determined as,

Thus, the gross pay is $ 447.425.

The total surface area Paul is required to paint is 36 yard square.

He needs to buy paint to cover all outside surfaces of his shed .

2 sides of shed are rectangles with a base of 12ft and a side of 6 ft.

Therefore,

area of a rectangle = lw

where

area of the rectangle = 12 × 6

area of the rectangle = 72 ft²

The rectangle are two.

Hence, area of the two rectangular faces = 72 + 72  = 144 ft²

The other two sides are squares with sides of 6 ft.

Therefore,

area of the two squares = 6² + 6² = 36 + 36 = 72 ft²

The roof consists of four triangles,

2 of the triangles have a base of 6 feet and a height of 6 feet.

Therefore,

area of the two triangles = 2 (1 / 2 × 6 × 6) = 36 ft²

The other two triangles have a base of 12 ft and a height of 6 ft.

area of the other triangle = 2(1 / 2 × 12 × 6) = 72 ft²

Hence,

total area the paint will cover = 72 + 36 + 72 + 144 = 324 ft² = 36 yard²

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To complete the perfect trinomial, we add (5/2)² to the given equation and get:

Subtracting 6 we get:

Therefore:

Finally, we get:

The question wants the "lowest common multiple" of 6 and 9, so first, lets find some of the miltiples of 6 and 9:

We can see that 18 is a commom multiple of 6 and 9, and is also the smallest, so the lowest common multiple of 6 and 9 is 18. So the least number of gift bags and bows that Rachel can buy is 18.

You can write the relation between distance and time, as follow:

y = kx

where y is the distance, x is the time and k is the constant of proportionality.

k can be obtained with the given information, as follow:

k = 90/30 = 3

Then, the equation of the relationship is:

y = 3x,

for a time of 10 seconds, the distance traveled is:

y = 3(10) = 30

Hence, the answer is:

y = 3x , 30 feet

EXPLANATION

Since the figure is like a pentagon, we need to add the interior angles in order to get the needed angle.

The first part of the figure is composed of a square with two right angles of 90 degrees and two angles of 135, making a total of 90+90+135+135 = 450 degrees.

The left needed angle should add a total of 540 degrees, by the Sum of Interior Angles of a Pentagon Theorem, as follows:

450 + bottom angle = 540

Subtracting -450 to both sides:

bottom angle = 540 - 450

Subtracting angles:

bottom angle = 90 degrees

In conclusion, the value of the bottom angle is 90 degrees.

The better deal between the offer at Mystic Bank and Four Rivers Bank is the deal at Mystic Bank.

In order to determine which bank has the better offer, the future value of the investment options have to be determined.

The future value of an investment is a function of the amount investment, the number of compounding, the years of the investment and the interest rate.

When an investment is compounded semi-annually, it means that it grows exponentially twice in a year. When an investment is compounded quarterly, it means that is grows exponentially four times in a year.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

Interest rate at Mystic bank = 10% /2 = 5%

Interest rate at Four Rivers Bank = 8% / 4 = 2%

Future value of the investment at Mystic bank :

$10,000 x (1.05)^(2 x 4) = $14,774.55

Future value of the investment at Four Rivers Bank :

$10,000 x (1.02)^(4 x 4) = $13,727.86

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to convert Fahrenheit to Celcius we have to apply the next formula:

C°= (F°-32) x 5/9

Replacing:

C = (103-32)x 5/9

C = 71 x 5/9

C = (71 x5)/9 = 355/9

If an oil-well contracted drills a shaft 7 meters deeper into the ground every 2 hours, then Graph H  best represents this rate.

The graphs are attached

Given that the oil-well contractor drills a shaft 7 meters deeper into the ground every 2 hours,

hence the rate at which the shaft drills = 7 meter / 2 hours = 3.5 meters per hour

Since the drill goes into the ground, hence the rate is negative that is -3.5 meters per hour

The slope (rate of change) of a line (m) is given by:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

a) For graph F, the line passes through the point (0,0) and (10, -20). Hence:

Slope of the line , [tex]m = \frac{-20 - 0}{10 - 0}[/tex]

Slope of the line is - 2 meters per hour

b) For graph G, the line passes through the point (0,0) and (10, -70). Hence:

Slope of the line, [tex]m = \frac{-70 - 0}{10 - 0}[/tex]

Slope of the line is -7 meters per hour

c) For graph H, the line passes through the point (0,0) and (10, -35). Hence:

Slope of the line, [tex]m = \frac{-35 - 0}{10 - 0}[/tex]

Slope of the line is -3.5 meters per hour

d) For graph J, the line passes through the point (0,-3.5) and (10, -3.5). Hence:

Slope of the line, [tex]m = \frac{-3.5 - 3.5}{10 - 0}[/tex]

Slope of the line is 0 meters per hour.

Therefore, if an oil-well contracted drills a shaft 7 meters deeper into the ground every 2 hours, then Graph H  best represents this rate.

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The question asks us to confirm the simplification of the expression:

Step 1: Factor the numbers

Therefore, the expression becomes:

Step 2: Cancel out the common terms from the expression

Step 3: Apply the rule of exponents

Therefore, we have:

CONCLUSION

The expression simplifies to give:

The answer is TRUE.

The probability of the sample mean is 0.2008.

What is probability?
Probability is the quality or state of being probable the extent to which something is likely to happen or be the case.

Sol-Let x be a continuous random variable that has a normal distribution with
μ=48 and σ=8
Thus,
X~N(48,8^2/16)
The standardized value of x is obtained by :
Z= X-48/√8^2/16~N(0,1)

The probability that the sample mean x for a random sample of 16 taken from this population will be between 49.62 and 52.80 can be obtained as:

P(49.62<x<52.80)

P=(49.62-48/√8^2/16<x-48/√8^2/16<52.80-48/√8^2/16)

=P(0.81<Z<2.4)

=P(Z<2.4)-P(Z<0.81)

=0.9918-0.7910

=0.2008
There for the probability is 0.2008.

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Answer:

The second one is the Multiplicative Property of Zero.
The fourth one is the Commutative property.

Answer:

The second and third one

Step-by-step explanation:

We will get 406 after multiplication .

What does multiply mean?

   58 * 7 = 406

We will get 406 after multiplying .

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4 basketballs

Explanation

Step 1

Ms. Banks divides 18 basketballs evenly among 3 bag

divide the 18 basketballs by 3 bags

Step 2

now, she takes 2 from each bag, so

Hence, the answer is 4 basketballs.

I hope this helps you